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no. 4
Cluster monomials in graph Laurent phenomenon algebras
Dantas e Moura, Guilherme Zeus1; Telekicherla Kandalam, Ramanuja Charyulu2; Woodruff, Dora3
1 University of Waterloo Department of Combinatorics and Optimization 200 University Avenue West Waterloo, ON N2L 3G1 (Canada)
2 University of Minnesota School of Mathematics 206 Church Street SE Minneapolis, MN 55455 (USA)
3 Massachusetts Institute of Technology Department of Mathematics 77 Massachusetts Avenue Cambridge, MA 02139 (USA)
Algebraic Combinatorics, Volume 8 (2025) no. 4, pp. 997-1019.

Laurent phenomenon algebras, first introduced by Lam and Pylyavskyy, are a generalization of cluster algebras that still possess many salient features of cluster algebras. Graph Laurent phenomenon algebras, defined by Lam and Pylyavskyy, are a subclass of Laurent phenomenon algebras whose structure is given by the data of a directed graph. In this paper, we prove that the cluster monomials of a graph Laurent phenomenon algebra form a linear basis, as conjectured by Lam and Pylyavskyy and analogous to a result for cluster algebras by Caldero and Keller. We also prove that, if the graph is a bidirected tree, the coefficients of the expansion of any monomial in terms of cluster monomials are nonnegative.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.433
Classification: 13F60
Keywords: Laurent phenomenon algebras, cluster algebras, graph LP algebras, positivity.

Dantas e Moura, Guilherme Zeus 1; Telekicherla Kandalam, Ramanuja Charyulu 2; Woodruff, Dora 3

1 University of Waterloo Department of Combinatorics and Optimization 200 University Avenue West Waterloo, ON N2L 3G1 (Canada)
2 University of Minnesota School of Mathematics 206 Church Street SE Minneapolis, MN 55455 (USA)
3 Massachusetts Institute of Technology Department of Mathematics 77 Massachusetts Avenue Cambridge, MA 02139 (USA)
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Dantas e Moura, Guilherme Zeus; Telekicherla Kandalam, Ramanuja Charyulu; Woodruff, Dora. Cluster monomials in graph Laurent phenomenon algebras. Algebraic Combinatorics, Volume 8 (2025) no. 4, pp. 997-1019. doi : 10.5802/alco.433. https://alco.centre-mersenne.org/articles/10.5802/alco.433/

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